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olga55 [171]
2 years ago
12

Find the circumference of the

Mathematics
1 answer:
WITCHER [35]2 years ago
6 0
The answer is abc deft hi
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5/18 x 3/4 simplify ​
Lesechka [4]

Answer:

5/24

Step-by-step explanation:

Find a common denominator and multiply, then convert to its simplest form.

3 0
2 years ago
HELLO!! :) CAN U PLEASE HELP ME WITH THIS PROBLEM? I WILL GIVE YOU BRAINLIEST AND A THANKS!! PLEASE EXPLAIN TOO!!
miskamm [114]

Answer:

21square feet

Step-by-step explanation:

Count the whole squares first.

if each square is one square foot then 18 whole squares will be 18×1= 18 square feet

add halves (aproximate halves) together. (3 in total)

Therefore A= 18 +3

= 21 square feet

3 0
2 years ago
Read 2 more answers
Enter an expression equivalent to (3x^2+2y^2-3x) + (2x^2+y^2-2x) - (x^2 + 3y^2 +x)
11111nata11111 [884]

Answer:

4x² - 6x

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

Distributive Property

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

(3x² + 2y² - 3x) + (2x² + y² - 2x) - (x² + 3y² + x)

<u>Step 2: Simplify</u>

  1. [Distributive Property] Distribute negative:                                                    3x² + 2y² - 3x + 2x² + y² - 2x - x² - 3y² - x
  2. Combine like terms (x²):                                                                                   4x² + 2y² - 3x + y² - 2x - 3y² - x
  3. Combine like terms (y²):                                                                                   4x² - 3x - 2x - x
  4. Combine like terms (x):                                                                                    4x² - 6x
4 0
3 years ago
The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell
emmasim [6.3K]

Answer:

a)

Highest (-3,-3)

Lowest (2,2)

b)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

a)

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12

completing the squares:

\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of  

\bf f(x,y)=x^2+y^2

subject to the constraint

\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0

Now we have

\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)

Let \bf \lambda be the Lagrange multiplier.

The maximum and minimum must occur at points where

\bf \nabla f=\lambda\nabla g

that is,

\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y

Replacing in the constraint

\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2

from this we get

<em>x=-1/2 + 5/2 = 2 or x = -1/2 - 5/2 = -3 </em>

<em> </em>

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

b)

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0
3 years ago
Suppose that 5 people sitting in a enclosed room are each generating about 500 BTUs of body heat per hour. If the room is 10 ft
Mazyrski [523]

Answer:

A)5

Step-by-step explanation:

I answered the question already.

4 0
3 years ago
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